Vertex degree sums for matchings in 3-uniform hypergraphs (Q2327218)

Summary: Let \(n, s\) be positive integers such that \(n\) is sufficiently large and \(s\le n/3\). Suppose \(H\) is a 3-uniform hypergraph of order \(n\) without isolated vertices. If \(\deg(u)+\deg(v) > 2(s-1)(n-1)\) for any two vertices \(u\) and \(v\) that are contained in some edge of \(H\), then \(H\) contains a matching of size \(s\). This degree sum condition is best possible and confirms a conjecture of the authors [Electron. J. Comb. 25, No. 3, Research Paper P3.45, 16 p. (2018; Zbl 1395.05136)], who proved the case when \(s= n/3\).